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Popular >

integral of 2-x-x^2

Solution

\int 2 - x - x^{2} d x

Solution

2 x - \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

\int 2 - x - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d x - \int x d x - \int x^{2} d x

\int 2 d x = 2 x

\int x d x = \frac{x ^{2}}{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 2 x - \frac{x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= 2 x - \frac{x ^{2}}{2} - \frac{x ^{3}}{3} + C

Popular Examples

integral of (x^3)/(sqrt(2+x^2))

\int \frac{x ^{3}}{2 + x ^{2}} d x

integral of ((x^3-x+3))/(x^2+x-2)

\int \frac{( x ^{3} - x + 3 )}{x ^{2} + x - 2} d x

integral of 15e^{3x}

\int 15 e^{3 x} d x

integral of sqrt(x)(x^3-1/(2x))

\int x (x^{3} - \frac{1}{2 x}) d x

integral of arctan(1-x)

\int arctan (1 - x) d x

Frequently Asked Questions (FAQ)

What is the integral of 2-x-x^2 ?
The integral of 2-x-x^2 is 2x-(x^2)/2-(x^3)/3+C